TY - GEN

T1 - Functional continuous Runge–Kutta methods for special systems

AU - Olemskoy, I. V.

AU - Eremin, A. S.

PY - 2016

Y1 - 2016

N2 - We consider here numerical methods for systems of retarded functional differential equations of two equations in which the right-hand sides are cross-dependent of the unknown functions, i.e. the derivatives of unknowns don’t depend on the same unknowns. It is shown that using the special structure of the system one can construct functional continuous methods of Runge–Kutta type with fewer stages than it is necessary in case of general Runge–Kutta functional continuous methods. Order conditions and example methods of orders three and four are presented. Test problems are solved, demonstrating the declared convergence order of the new methods.

AB - We consider here numerical methods for systems of retarded functional differential equations of two equations in which the right-hand sides are cross-dependent of the unknown functions, i.e. the derivatives of unknowns don’t depend on the same unknowns. It is shown that using the special structure of the system one can construct functional continuous methods of Runge–Kutta type with fewer stages than it is necessary in case of general Runge–Kutta functional continuous methods. Order conditions and example methods of orders three and four are presented. Test problems are solved, demonstrating the declared convergence order of the new methods.

KW - delay differential equations

KW - functional continuous Runge–Kutta

KW - structural methods

U2 - 10.1063/1.4951864

DO - 10.1063/1.4951864

M3 - Conference contribution

SN - 978-0-7354-1392-4

VL - 1738

BT - International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2015

PB - American Institute of Physics

T2 - International Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015

Y2 - 23 September 2015 through 29 September 2015

ER -